Inequalities for the eigenvectors associated to extremal eigenvalues in rank one perturbations of symmetric matrices
Résumé
This paper considers the eigenvectors involved in rank one perturbations of symmetric matrices. A doubly stochastic matrix based on the inner products between initial and perturbed eigenvectors is introduced to derive several relations for the latter ones. A majorization theorem used together with this doubly stochastic matrix provides the main results of the paper, which deal with the eigenvectors associated to the largest and smallest non-zero eigenval-ues. Further developments are also suggested for infinitesimal perturbations using convergent power expansions of both eigenvalues and eigenvectors. *
Origine : Fichiers produits par l'(les) auteur(s)
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